# CAT 2020 Quant Question [Slot 1] with Solution 19

Question

If a, b and c are positive integers such that ab = 432, bc = 96 and c < 9, then the smallest possible value of a + b + c is

1. 56
2. 59
3. 49
4. 46
Option: 4
Solution:

Given $ab = 432,bc = 96$ and $c < 9$

To find the minimum value for $a + b + c,$ the two larger numbers should be as close as possible.

The closest combination whose product is 432 is $18 \times 24$. For $b = 24,$ we get $c = 4$ and $a = 18$.

Hence the least value for $a + b + c = 46$.

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